Classify the possible combinations of signs for a reaction's δh and δs values by the resulting spontaneity

a. δh is positive and δs is negative

b. δh is positive and δs is positive

c. δh is negative and δs is positive

d. δh negative and δs is negative

for a, b, c and d find out which of following they are:

1. spontaneous as written at all temperatures

2. spontaneous in reverse at all temperatures

3. spontaneous as written above a certain temperature

4. spontaneous as written below a certain temperature

they can only have one answer but 2 can have the same answer

Answer :

(A) ΔH is positive and ΔS is negative  → (2) Spontaneous in reverse at all temperatures

(B) ΔH is positive and ΔS is positive  → (3) Spontaneous as written above a certain temperature

(C) ΔH is negative and ΔS is positive  → (1) Spontaneous as written at all temperatures

(D) ΔH negative and ΔS is negative → (4) Spontaneous as written below a certain temperature

Explanation :

According to Gibb's equation:

= Gibbs free energy  

= enthalpy change

= entropy change  

T = temperature in Kelvin

As we know that:

= +ve, reaction is non spontaneous

= -ve, reaction is spontaneous

= 0, reaction is in equilibrium

(A) ΔH is positive and ΔS is negative.

The reaction is non-spontaneous at all temperatures or spontaneous in reverse at all temperatures.

(B) ΔH is positive and ΔS is positive.

   (at low temperature)   (non-spontaneous)

   (at high temperature)   (spontaneous)

The reaction is spontaneous as written above a certain temperature.

(C) ΔH is negative and ΔS is positive.

The reaction is spontaneous as written at all temperatures

(D) ΔH is negative and ΔS is negative.

   (at high temperature)   (non-spontaneous)

   (at low temperature)   (spontaneous)

The reaction is spontaneous as written below a certain temperature.